In Isaac Deutscher's, The Prophet Armed: Trotsky 1879-1921, he writes of the youthful Trotsky:
His stay in Odessa ended in 1896. A realschule normally had seven forms but St. Paul's had only six so had to attend a similar school at Nikolayev to matriculate. He was now nearly seventeen but no political ideal had so far appealed to him. The year before Friedrich Engels had died; the event did not register in his mind of the future revolutionary - even the name of Karl Marx had not yet come to his ears. He was, in his own words, 'poorly equipped politically for a boy of seventeen at that time.' He was attracted by literature and was preparing for a university course in pure mathematics. These two approaches to life, the imaginative, and the abstract, lured him - later, he would strive to unite them in his writings ...
In the summer of 1896 he arrived at Nikolayev to complete his secondary education. He was lodging with a family whose sons had already been touched by socialist ideals. They drew him into argument and tried to impress their ideas on him. For several months they seemed to make no headway. He supercilious lay dismissed their 'Socialist Utopia'. Assailed with arguments he would adopt the posture of a somewhat conservative young man, not devoid of sympathy with the people but distrusting 'mob ideology' and 'mob rule'. His passion was for pure mathematics and he had no time or taste for politics ...
Q. There's no indication in Deutscher of what kind of direction Trotsky took in his thinking about mathematics. Is there any indication elsewhere?
Q. How did Trotsky attempts to unite the 'abstract' and the 'imaginative' in his writings?
I've read only a third of the first book and so it's possible that the answer may be later in the trilogy - but I think it's most likely that it isn't.